Numerical controls (NCs) are used in modern machine tools to control the positioning and movement of tools relative to a workpiece. To machine a workpiece in accordance with a stipulation, it may be necessary to move the tool relative to the workpiece on paths established beforehand. Therefore, this type of system may be described as a continuous-path control. The desired paths may be determined in a parts program that is executed by the numerical control. The numerical control may convert the geometrical instructions of the parts program into instructions for the positional control of the different axes of the machine tool.
To produce the parts program, CAD/CAM systems may be used to calculate tool paths from a predefined geometry of the body to be manufactured, taking into account, for example, the tool radius. Curved, continuously differentiable surfaces of the body to be manufactured are obtained by curvilinear, continuously differentiable curves in the tool path. They are approximated by polylines (or polygon curves) whose segments form non-continuously differentiable corners. A programmer may also create such parts programs directly, which, however, may be costly.
Thus, the machining of the workpiece is established in the parts program by the specification of the tool path. If one looks at this tool path more closely, it may be possible to divide the corners formed by the segments of the polyline into two categories. First of all, there are corners whose dimensional accuracy may be important for the later functioning of the workpiece, since edges of the workpiece are defined by these corners. However, there are also corners which may only be used to approximate curvilinear, continuously differentiable curves. The dimensional accuracy when executing these corners may not be as important here. A roundness of these corners may even prevent faceting of the actually smooth surface, the faceting developing due to the approximation by a polyline.
Since, namely, a machine tool is subject to certain restrictions with respect to the maximum acceleration and also the maximum jerk (change of acceleration) in its axes of motion, it is not possible to pass through a corner, provided in the parts program, between two segments of the tool path with a finite speed exactly, since to that end, an infinite acceleration would be necessary. Therefore, the maximum speed with which a corner may be traversed is a function of the maximum permissible tolerance with which the actual tool path may deviate from the ideal tool path. The greater this tolerance, the higher the possible speed. In this context, as speed increases, a corner established in the parts program becomes increasingly rounded. On the other hand, segments can be executed with an accuracy that is dependent only on the quality of the regulated drive system.
In a continuous-path control of the conventional type, a global corner tolerance acting on all corners of the tool path may be determined which, together with the mentioned parameters of maximum acceleration and maximum jerk, as well as the angle of the direction change from one segment of the tool path to the next segment, may establish the maximum permissible speed in the region of the corner.
European Published Patent Application No. 0 864 952 describes a method for machining a workpiece with maximum machining speed, for which the maximum permissible tolerance is taken into account. In that case, it may be possible to specify different tolerances for different regions of the tool path. However, when programming a tool path, it may be costly to indicate a smaller tolerance (edge tolerance) before each corner which leads to an edge in the contour of the workpiece, and to again specify a greater tolerance (curve tolerance) for the region then following, when only a continuously differentiable curve is being approximated by a polyline through the programmed corners. Therefore, usually only one tolerance is set for the execution of a polyline, namely, the smaller of the two tolerances.
The result is that paths having non-continuously differentiable corners are always executed with the edge tolerance, and thus in regions in which the greater curve tolerance would really be allowed, corners are executed with too low a speed. The machining time of the workpiece may therefore be unnecessarily great.